A student measures the diameter of a steel ball using a screw gauge. The true diameter of the ball is known to be 4.25 mm . The screw gauge has a pitch of 0.5 mm and 50 divisions on its circular scale. The instrument

Question

Quantrex Academy · Accepted Answer

Correct answer: A. 29

The least count (LC) of the screw gauge is given by:

\text{LC} = \dfrac{\text{Pitch}}{\text{Total circular divisions}} = \dfrac{0.5}{50} = 0.01 \text{ mm}

The true value of the measurement is related to the measured value and zero error by:

\text{True Value} = \text{Measured Value} - \text{Zero Error}

Substituting the given values:

4.25 = \text{Measured Value} - (+0.04)

\text{Measured Value} = 4.25 + 0.04 = 4.29 \text{ mm}

The measured value is also given by:

\text{Measured Value} = \text{MSR} + (\text{CSR} \times \text{LC})

Where MSR is the main scale reading and CSR is the circular scale reading.

4.29 = 4.0 + (\text{CSR} \times 0.01)

0.29 = \text{CSR} \times 0.01

\text{CSR} = 29

Thus, the

29^{\text{th}}

division coincides with the reference line.

Answer:

29

A student measures the diameter of a steel ball using a screw...

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